##### Chapter 5

## Statistics and Probability

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

#### Introduction

**Statistics and Probability**in brief. We hope this article helps you grasp the concept conveniently.

The addition rule of probability is the fourth rule. When at the same time, two events cannot occur then they are called disjoint or mutually exclusive. Let’s give you an example to enhance your understanding:

**Consider the following two events:**

C – a person has blood type AB+

D – a person has blood type A.

Now, if you consider both the events and if we assume that every person has only one blood type. Therefore it is impossible that events C and D will occur together. Here the event is said to be disjoint.

It is defined, as when two possible outcomes of an experiment are probable. It is called the binomial experiment. It is used to calculate the probability of success for binomial distributions. The formula is:-

**(x: n,p) = ^{n}Cxp^{x}q^{(n-x)}**

**n – Number of trials**

**p – Probability of success**

**q – Probability of failure**

**x – Number of success**

**b – Binomial Probability**

**Bayes Theorem **explains the probability of occurrence of an event related to any condition. It is also called the formula for the probability of causes. By making use of the definition of conditional probability and density, the **Bayes theorem** can be derived for the events and random variables. It is mostly used to find the reverse probabilities if the conditional probability is known of the event. The **Bayes theorem** formula is

**P(A|B) = P(A∩B) / P(B)**

As compared to the simple event, when an event consists of more than one single point of the sample space, then it is known as a compound event.

For example, if S = (45,65,76,88,90), E1 = (45, 88), E2 = (65,45,90) then E1 and E2 represent two compound events.

It refers to the probability of two or more independent events, both occurring at the same time. When an outcome of one event does not affect the outcome of another event, then that event is called an independent event. The formula is P(A and B) = P(A) × P(B)

There exists another event **E1′ **for every event E1 that shows the remaining elements of the sample space S.

**E1 = S − E1‘**

Concerning A when event B has already occurred that occurrence is probable of an event A, then it is known as **Conditional Probability**. The formula is

**P (A|B) = N(A∩B) / N(B). **

**P (A|B) – **It shows the probability of occurrence of A and B has already taken place,

**N (A∩B) – **Number of elements common to both A and B.

**N (B) – **it represents the number of elements in B which cannot be equal to zero.

Probability is all about chance. If the probability of any event is high, then it is likely to occur, and whose probability is low, then that event is unlikely to occur. Like if asked what will be the probability of getting a tail if a coin is tossed, you will say that there is a 50% probability of getting a tail. It is simply because you are aware of the fact that either it is head or tail.

**Formula **

**Probability of getting a tail**= No. of outcomes to get tail/No. of possible outcomes**Probability of a certain event**= No. of favourable outcomes/Total number of possible outcomes

**What is the probability and statistics in math?**

**Answer. **It is among the branches of mathematics that deals with analysis, interpretation, and with the laws controlling various events.

**What is the role of probability in statistics?**

**Answer. ** It is used to predict the results of many experiments having some assumptions. It is used to calculate the probability between prediction and results.

**What is the purpose of probability?**

**Answer. **It helps measure how likely something is to happen. It is mostly used to analyse the event and set possible results. Meteorologists too use probability to predict the weather as well.

**What are the four types of probability?**

**Answer. **The following are the four types of probability:

- Classical
- Empirical
- Subjective
- Axiomatic

**What is the statistics in math?**

**Answer. **It is a method in which probability theory is used. In other words, it is a collection, interpreting, and summarising of data. It is widely used by Mathematicians and statisticians.

**Statistics and Probability** are the two most important topics in Mathematics. Professionals widely use it, and business people to ascertain profit and loss; therefore, it becomes more important to understand this concept accurately.

We help you to comprehend **Statistics and Probability** first, with in-depth concept notes and explanatory video on the MSVGo app. MSVGo app has a video library that explains concepts with examples or explanatory visualisations or animation. To learn more about it, check out the MSVgo app. Stay tuned with the MSVGo app and happy learning!